Penerapan metode relaksasi Gauss-Seidel untuk menyelesaikan persamaan Schrӧdinger

• Main Authors: Nanik Andelita (Author), I Wayan Sudiarta (Author)
• Format: Book
• Published: Universitas Ahmad Dahlan, 2019-10-01T00:00:00Z.
• Subjects: article
• Online Access: Connect to this object online.

Summary

<p class="4Intisari"><strong>Abstrak. </strong>Metode numerik, seperti metode <em>finite difference</em>, <em>finite element</em> dan <em>Fourier,</em> untuk menyelesaikan persamaan Schrӧdinger telah banyak digunakan sebelumnya. Metode <em>finite difference time domain</em> (FDTD) telah dikembangkan oleh Sudiarta dan Geldart (2007). Metode FDTD telah berhasil diaplikasikan untuk berbagai sistem kuantum, satu partikel ataupun lebih. Salah satu kelemahan metode FDTD adalah pada kasus tertentu seperti potensial kotak dan potensial osilator harmonik ditemukan iterasi FDTD lebih lambat menuju konvergen sehingga memerlukan waktu komputasi yang lebih lama. Untuk mengatasi hal tersebut, metode relaksasi Gauss-Seidel digunakan. Pada paper ini, metode relaksasi diaplikasikan untuk menyelesaikan persamaan Schrӧdinger satu partikel pada berbagai potensial.</p><p class="4Intisari"> </p><strong>Abstract.</strong> Numerical methods, such as finite difference, finite element and Fourier methods to solve the Schrӧdinger equation have been used previously. The finite difference time domain (FDTD) method has been developed by Sudiarta and Geldart (2007). The FDTD method has been successfully applied to various quantum systems, for one particle or more. One of the weaknesses of the FDTD method is that in certain cases such as the box potential and harmonic oscillator it has been found that FDTD iterations are slower to converge and thus require longer computation time. To overcome this, the relaxation Gauss-Seidel method can be used. In this paper, the relaxation method was applied to solve the Schrӧdinger equation for one particle in various potential wells.

Item Description

2355-620X
10.12928/jrkpf.v6i2.14613